Standard Chartered PLC will pay a $300 million penalty to New York's financial regulator and impose measures to correct lapses in its anti-money-laundering procedures, the New York State Department of Financial Services said Tuesday, as part of a settlement with the British lender.

The deal, which had been expected this week, reflects the second time the New York state regulator has penalized Standard Chartered in recent years. The bank in 2012 paid $340 million to the office of Benjamin Lawsky, New York's superintendent...